{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2021:CPEKSTDBU4VOAJ7OIIR2L3FMEO","short_pith_number":"pith:CPEKSTDB","canonical_record":{"source":{"id":"2109.04304","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.LG","submitted_at":"2021-09-09T14:30:28Z","cross_cats_sorted":[],"title_canon_sha256":"0975f8c4a26c1535a05a3b4782bfdf8b864bca571c82989adb81eb21c09d2c15","abstract_canon_sha256":"d789cbd1e74ef2c736b865289b03f7a9bf4c268c9ace05374e000dd043a947d5"},"schema_version":"1.0"},"canonical_sha256":"13c8a94c61a72ae027ee4223a5ecac23be2b0e87c57f1ff0f450c7e94719ac3d","source":{"kind":"arxiv","id":"2109.04304","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2109.04304","created_at":"2026-07-05T03:12:57Z"},{"alias_kind":"arxiv_version","alias_value":"2109.04304v1","created_at":"2026-07-05T03:12:57Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2109.04304","created_at":"2026-07-05T03:12:57Z"},{"alias_kind":"pith_short_12","alias_value":"CPEKSTDBU4VO","created_at":"2026-07-05T03:12:57Z"},{"alias_kind":"pith_short_16","alias_value":"CPEKSTDBU4VOAJ7O","created_at":"2026-07-05T03:12:57Z"},{"alias_kind":"pith_short_8","alias_value":"CPEKSTDB","created_at":"2026-07-05T03:12:57Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2021:CPEKSTDBU4VOAJ7OIIR2L3FMEO","target":"record","payload":{"canonical_record":{"source":{"id":"2109.04304","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.LG","submitted_at":"2021-09-09T14:30:28Z","cross_cats_sorted":[],"title_canon_sha256":"0975f8c4a26c1535a05a3b4782bfdf8b864bca571c82989adb81eb21c09d2c15","abstract_canon_sha256":"d789cbd1e74ef2c736b865289b03f7a9bf4c268c9ace05374e000dd043a947d5"},"schema_version":"1.0"},"canonical_sha256":"13c8a94c61a72ae027ee4223a5ecac23be2b0e87c57f1ff0f450c7e94719ac3d","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-07-05T03:12:57.264591Z","signature_b64":"Ys1+yll8tgnMd9xtMtB7OxrAizGgy/bVKRpjWm3v458kpUQyDHIdxRW4ezF1Pskv5JhFWbYQppfszQYHf/fXBQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"13c8a94c61a72ae027ee4223a5ecac23be2b0e87c57f1ff0f450c7e94719ac3d","last_reissued_at":"2026-07-05T03:12:57.264112Z","signature_status":"signed_v1","first_computed_at":"2026-07-05T03:12:57.264112Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"2109.04304","source_version":1,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-07-05T03:12:57Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"eyAfCHAtbYpWv5+zDXK0kHRLzixncfWIoylT9iGhjxHsbYEABiLPfFdKb1gp94WB6Lgc7yv3V3IX3flw0MxzCg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-02T18:30:08.730960Z"},"content_sha256":"8fa40e54b85312bd994f625086c0f2e9825e0193d1dc4e988601d0c43b4f4ffc","schema_version":"1.0","event_id":"sha256:8fa40e54b85312bd994f625086c0f2e9825e0193d1dc4e988601d0c43b4f4ffc"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2021:CPEKSTDBU4VOAJ7OIIR2L3FMEO","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"DAE-PINN: A Physics-Informed Neural Network Model for Simulating Differential-Algebraic Equations with Application to Power Networks","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"cs.LG","authors_text":"Christian Moya, Guang Lin","submitted_at":"2021-09-09T14:30:28Z","abstract_excerpt":"Deep learning-based surrogate modeling is becoming a promising approach for learning and simulating dynamical systems. Deep-learning methods, however, find very challenging learning stiff dynamics. In this paper, we develop DAE-PINN, the first effective deep-learning framework for learning and simulating the solution trajectories of nonlinear differential-algebraic equations (DAE), which present a form of infinite stiffness and describe, for example, the dynamics of power networks. Our DAE-PINN bases its effectiveness on the synergy between implicit Runge-Kutta time-stepping schemes (designed "},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2109.04304","kind":"arxiv","version":1},"verdict":{"id":null,"model_set":{},"created_at":null,"strongest_claim":"","one_line_summary":"","pipeline_version":null,"weakest_assumption":"","pith_extraction_headline":""},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/2109.04304/integrity.json","findings":[],"available":true,"detectors_run":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938"},"references":{"count":0,"sample":[],"resolved_work":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57","internal_anchors":0},"formal_canon":{"evidence_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"author_claims":{"count":0,"strong_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"builder_version":"pith-number-builder-2026-05-17-v1"},"verdict_id":null},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-07-05T03:12:57Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"95EvqhUwsy3WfTtK0V+9sHP6J4LEGpzn/xTkrxn6rIig0fkeC6IxD8wip5GpP7JxQPeYxQn+g/JfO0q+f5zoAQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-02T18:30:08.731842Z"},"content_sha256":"b0b4e8afc50ec8113ec948fdf26826fceb8e4c4b56b7cef7b55e6619e2583307","schema_version":"1.0","event_id":"sha256:b0b4e8afc50ec8113ec948fdf26826fceb8e4c4b56b7cef7b55e6619e2583307"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/CPEKSTDBU4VOAJ7OIIR2L3FMEO/bundle.json","state_url":"https://pith.science/pith/CPEKSTDBU4VOAJ7OIIR2L3FMEO/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/CPEKSTDBU4VOAJ7OIIR2L3FMEO/bundle.json","status":"primary"}],"public_keys":[{"key_id":"pith-v1-2026-05","algorithm":"ed25519","format":"raw","public_key_b64":"stVStoiQhXFxp4s2pdzPNoqVNBMojDU/fJ2db5S3CbM=","public_key_hex":"b2d552b68890857171a78b36a5dccf368a953413288c353f7c9d9d6f94b709b3","fingerprint_sha256_b32_first128bits":"RVFV5Z2OI2J3ZUO7ERDEBCYNKS","fingerprint_sha256_hex":"8d4b5ee74e4693bcd1df2446408b0d54","rotates_at":null,"url":"https://pith.science/pith-signing-key.json","notes":"Pith uses this Ed25519 key to sign canonical record SHA-256 digests. Verify with: ed25519_verify(public_key, message=canonical_sha256_bytes, signature=base64decode(signature_b64))."}],"merge_version":"pith-open-graph-merge-v1","built_at":"2026-08-02T18:30:08Z","links":{"resolver":"https://pith.science/pith/CPEKSTDBU4VOAJ7OIIR2L3FMEO","bundle":"https://pith.science/pith/CPEKSTDBU4VOAJ7OIIR2L3FMEO/bundle.json","state":"https://pith.science/pith/CPEKSTDBU4VOAJ7OIIR2L3FMEO/state.json","well_known_bundle":"https://pith.science/.well-known/pith/CPEKSTDBU4VOAJ7OIIR2L3FMEO/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2021:CPEKSTDBU4VOAJ7OIIR2L3FMEO","merge_version":"pith-open-graph-merge-v1","event_count":2,"valid_event_count":2,"invalid_event_count":0,"equivocation_count":0,"current":{"canonical_record":{"metadata":{"abstract_canon_sha256":"d789cbd1e74ef2c736b865289b03f7a9bf4c268c9ace05374e000dd043a947d5","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.LG","submitted_at":"2021-09-09T14:30:28Z","title_canon_sha256":"0975f8c4a26c1535a05a3b4782bfdf8b864bca571c82989adb81eb21c09d2c15"},"schema_version":"1.0","source":{"id":"2109.04304","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2109.04304","created_at":"2026-07-05T03:12:57Z"},{"alias_kind":"arxiv_version","alias_value":"2109.04304v1","created_at":"2026-07-05T03:12:57Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2109.04304","created_at":"2026-07-05T03:12:57Z"},{"alias_kind":"pith_short_12","alias_value":"CPEKSTDBU4VO","created_at":"2026-07-05T03:12:57Z"},{"alias_kind":"pith_short_16","alias_value":"CPEKSTDBU4VOAJ7O","created_at":"2026-07-05T03:12:57Z"},{"alias_kind":"pith_short_8","alias_value":"CPEKSTDB","created_at":"2026-07-05T03:12:57Z"}],"graph_snapshots":[{"event_id":"sha256:b0b4e8afc50ec8113ec948fdf26826fceb8e4c4b56b7cef7b55e6619e2583307","target":"graph","created_at":"2026-07-05T03:12:57Z","signer":{"key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signer_id":"pith.science","signer_type":"pith_registry"},"payload":{"graph_snapshot":{"author_claims":{"count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57","strong_count":0},"builder_version":"pith-number-builder-2026-05-17-v1","claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"formal_canon":{"evidence_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"integrity":{"available":true,"clean":true,"detectors_run":[],"endpoint":"/pith/2109.04304/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"Deep learning-based surrogate modeling is becoming a promising approach for learning and simulating dynamical systems. Deep-learning methods, however, find very challenging learning stiff dynamics. In this paper, we develop DAE-PINN, the first effective deep-learning framework for learning and simulating the solution trajectories of nonlinear differential-algebraic equations (DAE), which present a form of infinite stiffness and describe, for example, the dynamics of power networks. Our DAE-PINN bases its effectiveness on the synergy between implicit Runge-Kutta time-stepping schemes (designed ","authors_text":"Christian Moya, Guang Lin","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.LG","submitted_at":"2021-09-09T14:30:28Z","title":"DAE-PINN: A Physics-Informed Neural Network Model for Simulating Differential-Algebraic Equations with Application to Power Networks"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2109.04304","kind":"arxiv","version":1},"verdict":{"created_at":null,"id":null,"model_set":{},"one_line_summary":"","pipeline_version":null,"pith_extraction_headline":"","strongest_claim":"","weakest_assumption":""}},"verdict_id":null}}],"author_attestations":[],"timestamp_anchors":[],"storage_attestations":[],"citation_signatures":[],"replication_records":[],"corrections":[],"mirror_hints":[],"record_created":{"event_id":"sha256:8fa40e54b85312bd994f625086c0f2e9825e0193d1dc4e988601d0c43b4f4ffc","target":"record","created_at":"2026-07-05T03:12:57Z","signer":{"key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signer_id":"pith.science","signer_type":"pith_registry"},"payload":{"attestation_state":"computed","canonical_record":{"metadata":{"abstract_canon_sha256":"d789cbd1e74ef2c736b865289b03f7a9bf4c268c9ace05374e000dd043a947d5","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.LG","submitted_at":"2021-09-09T14:30:28Z","title_canon_sha256":"0975f8c4a26c1535a05a3b4782bfdf8b864bca571c82989adb81eb21c09d2c15"},"schema_version":"1.0","source":{"id":"2109.04304","kind":"arxiv","version":1}},"canonical_sha256":"13c8a94c61a72ae027ee4223a5ecac23be2b0e87c57f1ff0f450c7e94719ac3d","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"13c8a94c61a72ae027ee4223a5ecac23be2b0e87c57f1ff0f450c7e94719ac3d","first_computed_at":"2026-07-05T03:12:57.264112Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-07-05T03:12:57.264112Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"Ys1+yll8tgnMd9xtMtB7OxrAizGgy/bVKRpjWm3v458kpUQyDHIdxRW4ezF1Pskv5JhFWbYQppfszQYHf/fXBQ==","signature_status":"signed_v1","signed_at":"2026-07-05T03:12:57.264591Z","signed_message":"canonical_sha256_bytes"},"source_id":"2109.04304","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:8fa40e54b85312bd994f625086c0f2e9825e0193d1dc4e988601d0c43b4f4ffc","sha256:b0b4e8afc50ec8113ec948fdf26826fceb8e4c4b56b7cef7b55e6619e2583307"],"state_sha256":"dc04dd0c2639b75fba5b2a3078373f15218e9904e34c9c562fa189517150afac"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"ADpswKkaEDf1k421Vyz4n39NgX9hWO0u87EmhOgpzSTpCzBm0DVibZT3JGIxcTA/goBK6vi4mtxoYESgy0fDCg==","signed_message":"bundle_sha256_bytes","signed_at":"2026-08-02T18:30:08.739014Z","bundle_sha256":"fcaf2488ec08baef89b4db8e0507999e9fb0a00eec28c40970b93f64e1974b67"}}